Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#22576193 | C2 | semidirect |
| 2. C2×#22576168 | C2 | semidirect |
| 4. #31774473 | C2 | semidirect |
| 5. #31774156 | C2 | semidirect |
| 6. #31774144 | C2 | semidirect |
| 7. #31774139 | C2 | semidirect |
| 8. #31774127 | C2 | semidirect |
| 9. #31773891 | C2 | semidirect |
| 10. C2×#22576083 | C2 | semidirect |
| 11. #428×C271 | C2 | semidirect |
| 77. M16×C271 | D4 | semidirect |
| 143. C271 | #3063 | semidirect |
| 153. #428 | D271 | semidirect |
| 210. M16 | D1084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576193 | 2 |
| C2×#22576168 | 2 |
| #31774478 | 2 |
| #31774473 | 2 |
| #31774156 | 2 |
| #31774144 | 2 |
| #31774139 | 2 |
| #31774127 | 2 |
| #31773891 | 2 |
| C2×#22576083 | 2 |
| #428×C271 | 2 |
| #3063 | 271 |